Optimal experimental design for mathematical models of haematopoiesis

Mathematics of neural stem cells: Linking data and processes

Adult stem cells are described as a discrete population of cells that stand at the top of a hierarchy of progressively differentiating cells. Through their unique ability to self-renew and differentiate, they regulate the number of end-differentiated cells that contribute to tissue physiology. The question of how discrete, continuous, or reversible the transitions through these hierarchies are and the precise parameters that determine the ultimate performance of stem cells in adulthood are the subject of intense research. In this review, we explain how mathematical modelling has improved the mechanistic understanding of stem cell dynamics in the adult brain. We also discuss how single-cell sequencing has influenced the understanding of cell states or cell types. Finally, we discuss how the combination of single-cell sequencing technologies and mathematical modelling provides a unique opportunity to answer some burning questions in the field of stem cell biology.

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

Chronic myeloid leukemia (CML) is a blood cancer characterized by dysregulated production of maturing myeloid cells driven by the product of the Philadelphia chromosome, the BCR-ABL1 tyrosine kinase. Tyrosine kinase inhibitors (TKIs) have proved effective in treating CML, but there is still a cohort of patients who do not respond to TKI therapy even in the absence of mutations in the BCR-ABL1 kinase domain that mediate drug resistance. To discover novel strategies to improve TKI therapy in CML, we developed a nonlinear mathematical model of CML hematopoiesis that incorporates feedback control and lineage branching. Cell-cell interactions were constrained using an automated model selection method together with previous observations and new in vivo data from a chimeric BCR-ABL1 transgenic mouse model of CML. The resulting quantitative model captures the dynamics of normal and CML cells at various stages of the disease and exhibits variable responses to TKI treatment, consistent with those of CML patients. The model predicts that an increase in the proportion of CML stem cells in the bone marrow would decrease the tendency of the disease to respond to TKI therapy, in concordance with clinical data and confirmed experimentally in mice. The model further suggests that, under our assumed similarities between normal and leukemic cells, a key predictor of refractory response to TKI treatment is an increased maximum probability of self-renewal of normal hematopoietic stem cells. We use these insights to develop a clinical prognostic criterion to predict the efficacy of TKI treatment and design strategies to improve treatment response. The model predicts that stimulating the differentiation of leukemic stem cells while applying TKI therapy can significantly improve treatment outcomes.

Systematic Bayesian posterior analysis guided by Kullback-Leibler divergence facilitates hypothesis formation

Bayesian inference produces a posterior distribution for the parameters of a mathematical model that can be used to guide the formation of hypotheses; specifically, the posterior may be searched for evidence of alternative model hypotheses, which serves as a starting point for hypothesis formation and model refinement. Previous approaches to search for this evidence are largely qualitative and unsystematic; further, demonstrations of these approaches typically stop at hypothesis formation, leaving the questions they raise unanswered. Here, we introduce a Kullback-Leibler (KL) divergence-based ranking to expedite Bayesian hypothesis formation and investigate the hypotheses it generates, ultimately generating novel, biologically significant insights. Our approach uses KL divergence to rank parameters by how much information they gain from experimental data. Subsequently, rather than searching all model parameters at random, we use this ranking to prioritize examining the posteriors of the parameters that gained the most information from the data for evidence of alternative model hypotheses. We test our approach with two examples, which showcase the ability of our approach to systematically uncover different types of alternative hypothesis evidence. First, we test our KL divergence ranking on an established example of Bayesian hypothesis formation. Our top-ranked parameter matches the one previously identified to produce alternative hypotheses. In the second example, we apply our ranking in a novel study of a computational model of prolactin-induced JAK2-STAT5 signaling, a pathway that mediates beta cell proliferation. Within the top 3 ranked parameters (out of 33), we find a bimodal posterior revealing two possible ranges for the prolactin receptor degradation rate. We go on to refine the model, incorporating new data and determining which degradation rate is most plausible. Overall, while the effectiveness of our approach depends on having a properly formulated prior and on the form of the posterior distribution, we demonstrate that our approach offers a novel and generalizable quantitative framework for Bayesian hypothesis formation and use it to produce a novel, biologically-significant insight into beta cell signaling.